How do you find the area between two lines?

First, find the x coordinates of where the lines intersect by setting the equations of the lines equal to each other. Then solve the quadratic (or polynomial) equation. Next, integrate both lines individually with the limits being the x coodinates of the intersection. Then subtract the area of the lower line from the area of the upper line to find the area between the two.

For example:

Find the area between y=4x and y=x- 2x + 5.

To find the x coordinates, set them equal to each other and solve.

So... 4x = x- 2x + 5 => 0 = x- 6x + 5. Thus using either the quadratic formula or factorising, we find that these lines intesect when x=1 and x=5

Next, we need to integrate the lines between the limits found.

So... y=4x integrates to => [2x2] and when plugging in x=5, we get 50 and x=1 gives us 2. Thus the area of y=4x bound by the x axis, x=1 and x=5 is 50-2 = 48.

Similarly, y=x- 2x + 5 integrates to => [x3/3 - x2 + 5x]. Again, we put in x=5 and it gives 125/3 and x=1 gives us 13/3. Thus the area of y=x- 2x + 5 bound by the x axis, x=1 and x=5 is 125/3 - 13/3 = 112/3.

We know by ploting the graphs that y=4x is above y=x- 2x + 5. Hence, to find the area between these two lines is 48 - 112/3 = 32/3.

Rory P. A Level Further Mathematics  tutor, A Level Maths tutor, GCSE...

2 years ago

Answered by Rory, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


Katrina M. IB Maths tutor, 13 Plus  Maths tutor, GCSE Maths tutor, A ...
£20 /hr

Katrina M.

Degree: Mathematics Bsc (Bachelors) - Exeter University

Subjects offered:Maths, Physics+ 2 more

Further Mathematics
-Personal Statements-

“Hi, I am a patient, experienced and enthusiastic tutor ready to help each student reach their full potential.”

£20 /hr

Luke B.

Degree: Mathematics (Masters) - Sheffield University

Subjects offered:Maths, Further Mathematics + 3 more

Further Mathematics
-Personal Statements-

“I am a fun, engaging and qualified tutor. I'd love to help you with whatever you need, giving you the support you need to be the best you can be!”

£20 /hr

Ioannis P.

Degree: Computer Science (Bachelors) - Warwick University

Subjects offered:Maths


“Maths and Computer Science are both my passion. Having tutored students in the past, they think that my methods seem very intuitive and natural; you will too.”

About the author

Rory P.

Currently unavailable: until 04/01/2016

Degree: Mathematics (Bachelors) - Imperial College London University

Subjects offered:Maths, Further Mathematics

Further Mathematics

“I am currently reading Mathematics at Imperial College London. I’m warm, patient, reliable but most of all, enthusiastic. My tutoring aim is to make you, the tutee, enjoy Maths and deliver exam success. Throughout sixth form, I helped...”

You may also like...

Other A Level Maths questions

Factorize completely x^3 - 6x^2 + 11x - 6

Find the coordinates of the minimum point of the curve y = 3x^(2) + 9x + 10

The line AB has equation 3x + 5y = 7. What is the gradient of AB?

Find the equation of the tangent to the curve y = 2 ln(2e - x) at the point on the curve where x = e.

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss